Functional Analysis of Air Temperatures as Related to Chilling Requirements of Perennial Fruit Crops

After more than two centuries of observation and research on chilling requirements of perennial fruit crops, there remain unresolved aspects concerning relationships between chilling condition and ambient air temperatures. The purpose of this ongoing study was to further explain association between chilling temperature and plant functions: growing, chilling, and freezing. Temperature data consisted of 5-year averages for 50 Mesonet weather sites randomly located throughout Kentucky. Based upon the Chilling Hours Model analysis, available chilling hours exceeded requirements of commonly grown perennial fruit crops. In the extended study, max and min daily temperatures were processed separately permitting their comparisons within plant functional classes. Nearly twice as many min as max temperature days were included within the chilling class function. Most consecutive days of chilling temperatures ranged from 1 to 3 days and were more clustered with min than max temperatures. Using multiple-year averages especially when the temperatures were near freezing point, resulted in a high percentage of individual years with freezing temperatures that were not reflected in the group average. Separating max and min temperatures in functional classes permitted greater focus on critical temperature-chilling relations. Within the chilling range, impact of min on chilling was nearly twice that of max. Contrariwise, widely reported research literature confirms that global warming has greater influence on min than on max or mean temperatures.


Chilling Is an Essential Process in Perennial Fruit Production
Since Knight's 1801 report on breaking plant dormancy, more than two centuries of research and observation have provided a workable knowledge of the genetic and physiological processes involved [1] [2]. However, given the added challenges resulting from the great diversity of plants and their environments, the increase in human population, and the presence of global warming, the need to understand and manage dormancy continues to be a critical factor in perennial fruit and nut crops. Winter dormancy is both a fruit production and a survival requirement for these crops. During the chilling period the plant undergoes changes necessary for flower and fruit production in the following season. Specific temperature levels and duration are required to break the chilling period permitting resumption of normal growth in the spring. When chilling temperature requirements are not met, plants may produce irregular leaves and flowers resulting in reduced or no crop production.

Chilling Models
Commonly used models for quantifying winter chill are based upon hourly temperature records. Four models, among several, have gained acceptance due to ease of use and adaption to different environmental conditions [3]. 1) Chilling Hours Model equates a chilling hour with a clock hour in which the air temperature is between 0˚C and 7.2˚C (32˚F and 45˚F). Freezing temperatures are not factored into winter chill calculation.
2) Utah Model is similar to Chilling Hour but assigns different chilling efficiencies to different temperature ranges.
3) Positive Utah Model is a modified version of the Utah developed for use in warmer climates.
4) The Dynamic Model postulates that chilling is a two-step process initiated by cool temperature and continuing into an intermediate product (chill portion) under warmer temperature.

Comparability of Chilling Models
Luedeling et al., (2009) [4] compared the four major models over 100 years of synthetic weather data. All models showed decrease in winter chill for all sites, but the extent of decrease varied with model. Luedeling and Brown (2011) [5] compared three models (Chilling Hours, Utah, and Dynamic) at 5078 weather stations around the world. The results varied substantially among models. The models were not proportional for chilling hours at different locations. They suggested need for conversion factors between winter chill models, and that further research efforts are needed to identify appropriate chilling models against the imminent effects of climate change.
schedules and statistical reporting units that affect validity of the outcome. Based upon testing of 12 climate models, Lobell et al. (2007) [11] found that weather change depended more upon changes in mean daily min or max than in combined daily means. Association between daily min was slightly greater than with daily max which was consistent with historical trends. Wilkens and Singh, (2001) [6] reported for quantities such as accumulated chill hours, response is different for min and max temperature as compared to mean daily temperature.
Based upon global studies of maximum and minimum temperature trends, Easterling et al. (1997) [7] determined that daily minimum temperature is increasing at a faster rate or decreasing at a slower rate, than the daily maximum, resulting in a decrease in diurnal temperature range for many parts of the world.
Objectives of the extended study were 1) To analyze air temperatures by plant functions: growing, chilling, and freezing. 2) To compare the impact of daily max and min temperatures on chilling hour production, and 3) To explore the effect of duration and frequency of chilling days on chilling hour production.

Materials and Methods
The present treatise is an extension of the study reported by Xue et al. (2016) [8] and is based on the same data for years and sites. Site identification numbers are identical for both studies permitting cross referencing. Additional relevant information for both studies included local and international locations of sites, elevation, precipitation, air temperature, and chilling hour production.
In the second study, the highest hourly temperature for each day in the month was averaged to give the max temperature per month; the lowest hourly temperature for each day in the month was measured to give the min temperature per month. These max and min temperatures were classified into three functional ranges and related to chilling requirements as follows: aa-Growing, both max and min above 7.2˚C; bb-chilling, both between 0˚C and 7.2˚C; cc-freezing, both below 0˚C; ab-max above 7.2˚C, min between 0˚C and 7.2˚C; ac-max above 7.2˚C, min below 0˚C; bc-max between 0˚C and 7.2˚C, min below 0˚C. Homo classes (aa, bb, cc) indicate that both max and min temperature were within the same range; hetero classes (ab, ac, bc) indicate that max and min temperature were in different ranges. Also, first and second letters specify max and min daily temperature; respectively. This classification system was applied to 5-year temperature means for each of the 50 Mesonet sites.
Linear correlation (Steel and Torrie, 1980) [9] was used to estimate relationships between chilling hour production (first study) and frequencies of max and

Results
Temperature classification by plant function was applied to data from the 50 sites resulting in 26.8% aa, 1.2% bb, 0.1% cc, 36.2% ab, 13.8% ac, and 22.0% bc (Table 1) Average daily max and min temperature by month are presented in Table 2.
Max and min temperatures had their highest average in September (24.4˚C to 13.3˚C) and their lowest average in January (5˚C and −2˚C). Max and min temperatures by month were significantly correlated indicating that changes in one were positively associated with changes in the other.
Temperatures within the chilling range (0˚C -7.2˚C) were further analyzed in relation to potential chilling hour production. Frequencies and durations of max and min temperatures within the chilling range were compared (Table 3) Linear correlations based on data in Table 1  and combined max/min temperatures (r = 0.986). Correlation was generally higher between temperature within the chilling range than with the total range.
It was observed that class c (freezing) occurred among some of the 5 years but was not apparent in the means for those years. Rather, the freezing temperature was masked by other years of larger, warmer temperatures. Since a single freezing temperature may kill developing buds, this phenomenon was explored using daily temperature in each of 5 months (December through April) for 5 years at

Discussion
The previous study [8], resulted in preliminary findings that chilling production Y. Xue et al.  Table 4. Number of days within months (December through April) in which one or more freezing temperatures (Class c) occurred among the 5 years but were masked by positive temperatures included within the mean. conditions. Furthermore, average chilling hours' production by sites (Table 1) was 1557 which by definition equals the number of clock hours or about 65 twenty-four hour days. It appeared more likely that the critical temperature initiated the chilling process which continued intermittingly as temperature permitted. This explanation is further supported by the homo bb being lower than the hetero, ab and ac, and by ab being greater than ac. These observations may provide support for the Dynamic Model including a two-step process initiated by cooler weather and continuing under warmer temperature.
Different temperature metrics were compared for their influence on chilling.
The highest hourly temperatures for each day in the month were averaged to get the max; the lowest hourly temperature for each day was averaged to get the min. These, temperatures were used to study relationships between max and min temperature with chilling temperature (Table 3). Of the total 115.4 days in which max and min temperatures were included in the chilling range, 62.4% were min and 37.6% were max. Thus, min contributed nearly twice that of max to chilling temperature. These findings support the emphasis on max and min indices as reported by other researchers [6] stated that daily max and min temperatures had major impact on plant growth and development. Lobell et al.
(2007) [11] concluded that quantities such as chill hours that are used in models to predict climate changes are more related to daily max and min when used separately than when averaged.
In the present study, max and min temperatures were based on 5-year means.
Since a mean is a single value that brings unequal quantities together into a best fitting number, it is possible that the impact of a critical component could be warming has greater negative impact on min than on max or mean temperature, whereas, chilling has a higher positive association with min than with max or mean temperature. Thus, as has been experienced, warming has a negative effect on chilling.

Conclusion
Continued investigation into relationships between chilling and temperature is warranted in view of the warming that has occurred and the unequivocal predictions (IPCC 2014) [15] that the warming trend is continuing. A more direct focus on temperature/chilling relationships was possible by using daily max and min rather than mean temperature and by dividing daily temperatures into plant functional classes: growing, chilling, and freezing. Within the chilling class, more min than max temperatures were associated with chilling. For studies involving temperatures fluctuating around 0˚C, the use of means may mask injurious freezing temperature. The smaller number of hours in the chilling class compared to the total number of chilling hours produced, may support the Dynamic Chilling Model which postulates a two-step process initiated by cooler and increased by warmer temperature. However, further research on initiation and duration of chilling conditions is necessary.